The cross-talk cancellation problem
is in a sense the ultimate sound reproduction problem since an efficient
cross-talk canceller gives one complete control over the sound field at
a number of "target" positions.

The objective of a cross-talk canceller
is to reproduce a desired signal at a single target position while cancelling
out the sound perfectly at all remaining target positions. The basic principle
of cross-talk cancellation using only two loudspeakers and two target positions
has been known for more than 30 years. In 1966, Atal and Schroeder used
physical reasoning to determine how a cross-talk canceller comprising only
two loudspeakers placed symmetrically in front of a single listener could
work. In order to reproduce a short pulse at the left ear only, the left loudspeaker first emits a positive pulse. This pulse
must be cancelled at the right ear by a slightly weaker negative pulse
emitted by the right loudspeaker. This negative pulse must then be cancelled
at the left ear by another even weaker positive pulse emitted by the left
loudspeaker, and so on. Atal and Schroeder's model assumes free-field conditions;
the influence of the listener's torso, head and outer ears on the incoming
sound waves are ignored.

The graphic demonstrates the cross-talk
cancellation principle under free-field conditions when the two loudspeakers span 60 degrees as seen by the listener (this corresponds to the loudspeaker
setup recommended for listening to conventional stereo material such as pop music). Note that the "zone of cross-talk cancellation" is very small.